arXiv research

A method to identify important features without solving the full problem.

The study examines the asymptotic behavior of extremal length in Teichmüller space.

Modern detectors of cosmic gamma-rays are a special type of imaging telescopes (air Cherenkov telescopes) supplied with cameras with a relatively large number of photomultiplier-based pixels. For example, the camera of the TAIGA-IACT telescope has 560 pixels of hexagonal structure. Images in such cameras can be analyse…

Sharp inequalities and extremizers for J functional on Kähler manifolds.

The paper introduces twins in Kähler and Sasaki geometry, generalizing known concepts.

GraphXCOVID uses deep semi-supervised learning to identify COVID-19 from chest X-rays with minimal labels.

Paper develops a novel approach to identify clusters of features in multivariate extremes.

The task of classifying X-ray data is a problem of both theoretical and clinical interest. Whilst supervised deep learning methods rely upon huge amounts of labelled data, the critical problem of achieving a good classification accuracy when an extremely small amount of labelled data is available has yet to be tackled.…

We determine the asymptotic behaviour of extremal length along arbitrary Teichmüller rays. This allows us to calculate the endpoint in the Gardiner-Masur boundary of any Teichmüller ray. We give a proof that this compactification is the same as the horofunction compactification. An important subset of the latter is the…

Deep learning techniques, namely convolutional neural networks (CNN), have previously been adapted to select gamma-ray events in the TAIGA experiment, having achieved a good quality of selection as compared with the conventional Hillas approach. Another important task for the TAIGA data analysis was also solved with CN…

Rare Teichmüller disks converge to small limit sets.

A robust algorithm for non-negative matrix factorization (NMF) is presented in this paper with the purpose of dealing with large-scale data, where the separability assumption is satisfied. In particular, we modify the Linear Programming (LP) algorithm of [9] by introducing a reduced set of constraints for exact NMF. In…

Concept bottleneck models enable concept manipulation for model interpretation.

In the present paper we prove that, on a hyperkähler manifold, walls of the kähler cone and extremal rays of the Mori cone are determined by all divisors satisfying certain numerical conditions.

Early results in using convolutional neural networks (CNNs) on x-rays to diagnose disease have been promising, but it has not yet been shown that models trained on x-rays from one hospital or one group of hospitals will work equally well at different hospitals. Before these tools are used for computer-aided diagnosis i…

We show that grafting any fixed hyperbolic surface defines a homeomorphism from the space of measured laminations to Teichmuller space, complementing a result of Scannell-Wolf on grafting by a fixed lamination. This result is used to study the relationship between the complex-analytic and geometric coordinate systems f…

Study identifies COVID-19 pneumonia from chest X-rays.

For a given lattice, we establish an equivalence involving a closed zone of the corresponding Voronoi polytope, a lamina hyperplane of the corresponding Delaunay partition and a quadratic form of rank 1 being an extreme ray of the corresponding L-type domain.

New method identifies cluster representatives with minimal pulls.

We study the problem of recovery both the attenuation $a$ and the source $f$ in the attenuated X-ray transform in the plane. We study the linearization as well. It turns out that there are natural Hamiltonian flow that determines which singularities we can recover. If the perturbations $δa$, $δf$ are supported in a com…

Analyzing large X-ray diffraction (XRD) datasets is a key step in high-throughput mapping of the compositional phase diagrams of combinatorial materials libraries. Optimizing and automating this task can help accelerate the process of discovery of materials with novel and desirable properties. Here, we report a new met…

Lung segmentation from abnormal CXRs using data imputation.

An extreme wind speed estimation method that considers wind hazard climate types is critical for design wind load calculation for building structures affected by mixed climates. However, it is very difficult to obtain wind hazard climate types from meteorological data records, because they restrict the application of e…

One challenge impeding the analysis of terabyte scale x-ray scattering data from the Linac Coherent Light Source LCLS, is determining the number of clusters required for the execution of traditional clustering algorithms. Here we demonstrate that previous work using bi-cross validation (BCV) to determine the number of …

Study of tangent bundle positivity on complex projective varieties.

Researchers found multiple ways to end-sum 4-manifolds, contradicting a previous conjecture.

The study classifies Fano varieties with specific pseudoindex.

We compute the class of the closure of the locus of canonical divisors in the projectivization of the Hodge bundle $\mathbb{P}\overline{\mathcal{H}}_g$ over $\overline{\mathcal{M}}_g$ which have a zero at a Weierstrass point. We also show that the strata of canonical and bicanonical divisors with a double zero span ext…

New asymmetric metric on Teichmüller space for surfaces.

We consider random walks on locally compact groups, extending the geometric criteria for the identification of their Poisson boundary previously known for discrete groups. First, we prove a version of the Shannon-McMillan-Breiman theorem, which we then use to generalize Kaimanovich's ray approximation and strip approxi…

Proves uniqueness of certain spacetime solutions with extremal horizons.

Let $E$ be a flat complex vector bundle over a closed oriented odd dimensional manifold $M$ endowed with a flat connection $\nabla$. The refined analytic torsion for $(M,E)$ was defined and studied by Braverman and Kappeler. Recently Mathai and Wu defined and studied the analytic torsion for the twisted de Rham complex…

Let $\mathcal{W}^{n}$ be the class of $C^{\infty }$ complete simply connected $n-$dimensional manifolds without conjugate points. The hyperbolic space as well as Euclidean space are good examples of such manifolds. Let $$ and let $A$ be a subset of $W$. This article aims at characterization and bu…

Inference over tails is usually performed by fitting an appropriate limiting distribution over observations that exceed a fixed threshold. However, the choice of such threshold is critical and can affect the inferential results. Extreme value mixture models have been defined to estimate the threshold using the full dat…

This study examines whether PCA can effectively identify nitrogen pollution sources in rivers.

This paper considers the problem of Phase Identification in power distribution systems. In particular, it focuses on improving supervised learning accuracies by focusing on exploiting some of the problem's information theoretic properties. This focus, along with recent advances in Information Theoretic Machine Learning…

With the development and widespread use of wireless devices in recent years (mobile phones, Internet of Things, Wi-Fi), the electromagnetic spectrum has become extremely crowded. In order to counter security threats posed by rogue or unknown transmitters, it is important to identify RF transmitters not by the data cont…

Study extends geodesic ray transform results to orientable surfaces.

Let (X,[ω]) be a compact Kaehler manifold with a fixed Kaehler class [ω]. Let K_ωbe the set of all Kaehler metrics on X whose Kaehler class equals [ω]. In this paper we investigate the critical points of the functional Q(g)= |v|_g T_0(X,g)^{1/2} for g \in K_ω, where v is a fixed nonzero vector of the determinant line λ…

In this note we propose to show that the Kähler-Ricci flow fits naturally within the context of the Minimal Model Program for projective varieties. In particular we show that the flow detects, in finite time, the contraction theorem of any extremal ray and we analyze the singularities of the metric in the case of divis…

Study shows non-polyhedral structure in moduli spaces for n≥8.

In this paper we study K-polystability of arbitrary (possibly non-projective) compact Kähler manifolds admitting holomorphic vector fields. As a main result, we show that existence of a constant scalar curvature Kähler (cscK) metric implies 'geodesic K-polystability', in a sense that is expected to be equivalent to K-p…

First order methods can take extremely long to find global minima of non-convex functions.

Cryptocurrency markets show higher spreads during extreme fear and greed phases.

Study lenient regret and good-action identification in Gaussian process bandits.

Ray-Singer torsion is a mathematical concept with applications in physics.

We provide an explicit resolution of the existence problem for extremal Kaehler metrics on toric 4-orbifolds M with second Betti number b2(M)=2. More precisely we show that M admits such a metric if and only if its rational Delzant polytope (which is a labelled quadrilateral) is K-polystable in the relative, toric sens…

De-identification of clinical records is an extremely important process which enables the use of the wealth of information present in them. There are a lot of techniques available for this but none of the method implementation has evaluated the scalability, which is an important benchmark. We evaluated numerous deep le…